Static Arbitrage Bounds on Basket Option Prices

Mathematics arXiv Working Paper No. math.OC/0302243

19 Pages Posted: 12 Jul 2004

See all articles by Alexandre d'Aspremont

Alexandre d'Aspremont

Princeton University - Department of Operations Research and Financial Engineering

Laurent El Ghaoui

University of California, Berkeley - Department of Electrical Engineering & Computer Sciences (EECS)

Date Written: February 19, 2003

Abstract

We consider the problem of computing upper and lower bounds on the price of a European basket call option, given prices on other similar baskets. Although this problem is very hard to solve exactly in the general case, we show that in some instances the upper and lower bounds can be computed via simple closed-form expressions, or linear programs. We also introduce an efficient linear programming relaxation of the general problem based on an integral transform interpretation of the call price function. We show that this relaxation is tight in some of the special cases examined before.

Keywords: Basket options, static arbitrage, linear programming

JEL Classification: C61, C63, G12

Suggested Citation

d'Aspremont, Alexandre and El Ghaoui, Laurent, Static Arbitrage Bounds on Basket Option Prices (February 19, 2003). Mathematics arXiv Working Paper No. math.OC/0302243, Available at SSRN: https://ssrn.com/abstract=563443 or http://dx.doi.org/10.2139/ssrn.563443

Alexandre D'Aspremont

Princeton University - Department of Operations Research and Financial Engineering ( email )

Princeton, NJ 08544
United States

Laurent El Ghaoui (Contact Author)

University of California, Berkeley - Department of Electrical Engineering & Computer Sciences (EECS) ( email )

Berkeley, CA 94720-1712
United States